What is the value of `(3.7)^(2) - (1.7)^(2)` ?

Options

A. 5.4
B. 10.8
C. 7.2
D. 9.6

Answer

To solve the problem \( (3.7)^2 - (1.7)^2 \), we can use the difference of squares formula, which states that:

\[ a^2 - b^2 = (a - b)(a + b) \]

In this case, let \( a = 3.7 \) and \( b = 1.7 \).

### Step 1: Calculate \( a - b \) and \( a + b \)

1. **Calculate \( a - b \)**:
\[ 3.7 - 1.7 = 2.0 \]

2. **Calculate \( a + b \)**:
\[ 3.7 + 1.7 = 5.4 \]

### Step 2: Use the difference of squares formula

Now, substitute \( a - b \) and \( a + b \) into the difference of squares formula:

\[ (3.7)^2 - (1.7)^2 = (3.7 - 1.7)(3.7 + 1.7) = (2.0)(5.4) \]

### Step 3: Calculate the product

Now, calculate the product:

\[ 2.0 \times 5.4 = 10.8 \]

### Final Answer

Thus, the value of \( (3.7)^2 - (1.7)^2 \) is \( \boxed{10.8} \).

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